Question

find the Riemann sum for f(x)=x^2+x over the interval(0,8),where x0=0,x1=1,X2=3,X3=7,X4=8,and where c1=1,c2=2,c3=5 and c4=8

Answer 1

What are c's??

Answer 2

center??

Answer 3

\(\sum_{[x_n-x_{n-1}]} f(x) dx\)
now, at c1= 1, f(1) = 1^2 +1 =2
and \(\triangle x= 1-0 =1\)
hence, the first term is 2*1
the second term:
at c2= 2, f(2) =2^2+2 = 6
and \(\triangle x = 3-1=2\)
hence the second term is 6*2 =12
do the same with the third term and the fourth term
add them together. done